If $$x \ne 2$$ and $$x \ne 6$$, then $$\displaystyle \frac{x^2+4x-12}{x^2 - 8x + 12} = $$

Before we go any further, did you notice that this is a __Plugging In__ question?

Incorrect.
In order for a fraction to equal 1, the bottom (the denominator) and the top (the numerator) need to be the same.
If you tried to __Plug In__ a good number such as 2, you overlooked the fact that the bottom of the fraction becomes 0. Dividing by 0 is illegal in GMAT Land. __Plug In__ different numbers that fit the problem.

Incorrect.
In order for a fraction to equal -1, the bottom (the denominator) and the top (the numerator) need to be the same, with one of them being the negative of the other. In this case, bottom and top aren't the same to begin with.
If you __Plugged In__ $$x=0$$, you must have tried to be smart and get rid of all the $$x$$'s in the problem. But remember, you need to check all five answer choices before you take your pick.

Incorrect.
In order for a fraction to equal $$\frac{1}{2}$$, the bottom (the
denominator) needs to be twice as much as the top (the numerator). This is not the case. __Plug In__ a good number, such as $$x=3$$, into the problem. Your target is -3. Check all five answer choices. This one is wrong. __POE__ and move on!

Incorrect.
Simply __Plug In__ a good number, such as $$x=3$$, into the question. Your target is -3.
Check all five answer choices. This one is wrong. __POE__ and move on!

Okay. The program will target you with more __Plugging In__ questions in the future. Look for opportunities to Plug In. The surefire sign to Plug In is __variables in the answer choices__.

Good.
The surefire sign to __Plug In__ is __variables in the answer choices__.

Correct.
Even difficult math expressions become simple when you __Plug In__ numbers instead of the variables. Try $$x=3$$.
> $$\displaystyle \frac{x^2+4x-12}{x^2 - 8x + 12} = \frac{(3)^2+4(3)-12}{(3)^2 - 8(3) + 12}$$
>>>> $$\displaystyle = \frac{9+12-12}{9 - 24 + 12}$$
>>>> $$\displaystyle = \frac{9}{-3}$$
>>>> $$\displaystyle = -3$$
So your **goal value** is -3. Plug in $$x=3$$ into all the answer choices and eliminate those that do not match your goal value of -3. Be sure check all five answer choices before you take your pick.
Answer choice D is the only answer that matches -3.
> $$\displaystyle \frac{x+6}{x-6} = \frac{3+6}{3-6} = \frac{9}{-3} = -3$$

$$-1$$

$$1$$

$$\displaystyle \frac{x}{2}$$

$$\displaystyle \frac{x+6}{x-6}$$

$$\displaystyle \frac{x+12}{x-12}$$

Sure I did.

No. I could use some brushing up regarding identifying __Plugging In__ questions.

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